(A)Tip: Read the entire question carefully.
If you ignore the cube root in the second equation and solve \(b^{y}=b^{5}\) instead of \(\sqrt[3]{b^{y}} = b^{5}\), you will get \(y=5\). Then \(y-x=5-6=-1\). But this is wrong.

(B)Tip: Read the entire question carefully.
If you solve for \(x\), instead of \(y-x\), you will get this wrong answer.

(D)Tip: Know the Rules of Exponents.
If you apply the wrong formula \(a^{m} \cdot a^{n} = a^{\boxed{m \cdot n}}\) to the first equation, like this:

(C)Tip: Read the entire question carefully.
If you forget the \(0\) in the multiplicand's exponent and read \(\frac{(3y^{3})(2y^{2})^{2}}{(y^{4})^{3}} \cdot (y)^{3}\) instead of \(\frac{(3y^{3})(2y^{2})^{2}}{(y^{4})^{3}} \cdot (y^{\boxed{0}})^{3}\), you will get this wrong answer.

(D)Tip: Know the Rules of Exponents.
If in step \((7)\) you apply the wrong rule \((a^{n})^{m}=a^{\fbox{n + m}}\) to the denominator, as shown below, you will get this wrong answer. Don't add the exponents when you should be multiplying them.

(E)Tip: Know the Rules of Exponents.Tip: Be careful with signs!
If in the step \((9)\) you apply the wrong rule \(\frac{a^{m}}{a^{n}}=a^{\fbox{n-m}}\), you will get this wrong answer. The correct rule states \(\frac{a^{m}}{a^{n}}=a^{m-n}\).

Alternatively, you may not notice or you may forget that the exponent becomes negative. Be careful!

Review

If you thought these examples difficult and you need to review the material, these links will help: